Transient Reward Approximation for Continuous-Time Markov Chains
For researchers in reliability and performance analysis, this provides a scalable method for analyzing large CTMCs with many rates, avoiding limitations of multi-terminal decision diagrams.
The paper addresses the analysis of very large continuous-time Markov chains with many distinct rates, using abstraction and novel algorithms to compute bounds on expected rewards. The approach is demonstrated to be practical and efficient on two case studies.
We are interested in the analysis of very large continuous-time Markov chains (CTMCs) with many distinct rates. Such models arise naturally in the context of reliability analysis, e.g., of computer network performability analysis, of power grids, of computer virus vulnerability, and in the study of crowd dynamics. We use abstraction techniques together with novel algorithms for the computation of bounds on the expected final and accumulated rewards in continuous-time Markov decision processes (CTMDPs). These ingredients are combined in a partly symbolic and partly explicit (symblicit) analysis approach. In particular, we circumvent the use of multi-terminal decision diagrams, because the latter do not work well if facing a large number of different rates. We demonstrate the practical applicability and efficiency of the approach on two case studies.